-12x^2-3x=-8x^2-22

Solution for -12x^2-3x=-8x^2-22 equation:

-12x^2-3x=-8x^2-22

We move all terms to the left:

-12x^2-3x-(-8x^2-22)=0

We get rid of parentheses

-12x^2+8x^2-3x+22=0

We add all the numbers together, and all the variables

-4x^2-3x+22=0

a = -4; b = -3; c = +22;
Δ = b2-4ac
Δ = -32-4·(-4)·22
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-19}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*-4}=\frac{22}{-8}
=-2+3/4
$